# 5 Repeatedly Asked Questions From Average

Q.1 Abhay married at the age of 26 years 9 years ago. At the time of the marriage his wife was 23 years old. After 7 years the average age of Abhay, his wife and their two daughters is 14 years. The difference between the ages of his two daughters is 1 year. Find the age of both daughters.
A. 2,3
B. 4,5
C. 3,4
D. 5,6
E. None of these

Q.2 The average weight of 18 workers is 50 kg. A new worker replaced an old worker whose weight is 45 kg. Hence, the average weight of the workers increased by 1 kg. What is the ratio between the old workman and new workman?
A. 23:25
B. 11:12
C. 5:7
D. 3:4
E. None of these

Q.3 There are seven consecutive positive even numbers. The average of the square of the first and the last number is 712. Find the 2nd largest number.
A. 26
B. 22
C. 25
D. 20
E. 30

Q.4 The average age of all 15 members in a family is 30 years. The ratio between male and female is 3:2. If the total age of men is the 16/25 of the total age of family. Find the average age of women.
A. 25 years
B. 27 years
C. 30 years
D. 32 years
E. None of these

Q.5 In Mahesh’s opinion, his age is greater than 56 years but less than 63 years. His sister thinks that his age cannot be greater than 59 years and his mother’s view his age is greater than 51 years but less than 60 years. What is his average age?
A. 55 years
B. 52.5 years
C. 51 years
D. 57 years
E. 58 years

## Solution:

#### 1. Ans. D.

Solution:
After 7 years of the marriage the age of Abhay was = 33 years, His wife’s age= 30
Age of daughters= x, x+1  70=64+2x
70-64=2x
6=2x
x=3
Age of daughters
3+2=5
3+1+2=6

#### 2. Ans. C.

Solution:
Total of 18 workers= 18×50=900
New average=51 years 51×18=900-45+x
918-900+45=x
x=63
Ratio=45:63
=5:7

#### 3. Ans. E.

Solution:
Let, Seven consecutive even number= x, x+2, x+4, x+6, x+8, x+10, x+12 1424=x2+x2+144+24x
2x2+24x-1280=0
x2+12x-640=0
x2+(32-20)x-640=0
x2+32x-20x-640=0
x(x+32)-20(x+32)=0
(x+32)(x-20)=0
x=-32,20
2nd largest number= x+10
=20+10=30

#### 4. Ans. B.

Solution:
Total age= 15×30=450
Male=15×3/5=9
Female=15×2/5=6
Total age of men= 16/25×450
=288
Total age of women=450-288
=162
Average of women= 162/6=27 years

#### 5. Ans. E.

Solution:
Let Mahesh age=x
In Mahesh’s opinion his age= 56<x<62
In his sister's opinion his age=59>=x
In his mother, opinion his age=51<x<60
Average= (57+58+59)/3
=58 years 